The spicy chili pepper known most famously in Mexican and Indian cuisines is indeed cayenne, though it is also red. There is no distinction between cayenne and red pepper aside from the name. Some manufacturers use one name over the other to distinguish the grade of "heat" of the pepper powder, but this distinction is not universal. To clear any confusion in the kitchen, if a recipe calls for cayenne, it means red, and if it calls for red, it means cayenne. They are unmistakably interchangeable.
Cayennne pepper and red pepper refer to the same product; a hot, red native to parts of South and Central America, though they are prominent in Asian and Middle Eastern cuisine. The botanical name for cayenne/red pepper is capsicum minimum or baccatum. Also in the capsicum family are the familiar bell and jalapeño peppers. The process for creating cayenne/red pepper entails a series of dehydration stages; the peppers are dried, ground, baked, ground again for fineness and sifted. The product is the dusty red/orange spice powder that, according to the American Spice Trade Association, is termed "Red Pepper" rather than cayenne as a more generic name. The name cayenne is used by some producers to refer to a red pepper with greater heat. There are varying "heat" grades of cayenne/red pepper, though they are still one in the same.
A variety of peppers are used to produce cayenne/red pepper, and though there are subtle distinctions, the peppers come in varieties of colors (reds, yellows and oranges), sizes and heat levels. The color variance in cayenne/red pepper is due to the beta carotene level of the pepper used for production. The lighter, more orange or yellow a shade of ground pepper, the greater the beta carotene levels. This does not imply, however, that the darker brown or red pepper powder is any less healthy.
A cayenne/red pepper's "heat" is measured in a unit known as a Scoville (SHU: Scoville Heat Unit). This classification is used by the American Spice Trade Association. The SHU measures the capsaicin (element responsible for heat) in cayenne/red pepper. The amount of capsaicin develops at variant levels of any one pepper fruit. The SHU in cayenne/red pepper ranges from 30,000 to 50,000, but there are varieties that can have up to 140,000 SHUs.
Chili peppers are indigenous to Mexico, Central and South America and the West Indies. The pepper did not reach Europe and Asia until the "discovery" of the Americas in the 16th century. Chili peppers were taken back to Europe, from where they were introduced to Asia through the spice trade. Chili pepper is a prominent ingredient in Indian cuisine, a result of the early Portuguese settlements. The pepper eventually found its way throughout central, southern, and eastern Asia as the warm climate is conducive to its cultivation.
The main uses of cayenne/red pepper are for culinary purposes, though the spice has been identified and used as an herbal medicine. The spice is the characteristic flavor of Mexican, Creole, Cajun, Thai, Indian and Szechuan cooking. Suggested uses include pepper spiced roasted nuts, stir fry or rice dishes, in barbecue or steak sauce or added to chocolate.
Aside from the confusion between "Red" and "Cayenne," the spicy powder is also known as Guinea powder in reference to where European settlers first discovered it. The name Cayenne derives from the Cayenne region of French Guiana, which is derived from the Tupi Indian language. Yet another name for cayenne/red pepper is "bird pepper."